Analyze Phase
Analyze tests causal hypotheses and quantifies relationships. The exam asks you to choose the right graphical or statistical tool, check assumptions, and separate statistical significance from practical importance.
Core rules
- Use process maps, fishbone diagrams, 5 Whys, and FMEA to generate hypotheses, then verify them with data. A fishbone is not proof of a root cause.
- Stratify before testing: by shift, line, supplier, operator, time, or customer segment. Pareto, multi-vari, boxplots, and scatterplots often reveal the pattern.
- State H0 and H1. Choose the test by data type and design: two-group continuous data uses a two-sample t-test or Mann-Whitney; three or more groups use ANOVA or Kruskal-Wallis; proportions use chi-square; paired before-after data use a paired test; continuous X-Y relationships use correlation or regression.
- Check independence, normality or residual behavior, and equal variance. If assumptions fail, use a nonparametric test, transform, or different model.
- Use confidence intervals and effect size, not only p-values. Power and sample size affect whether a real effect can be detected.
Worked example
A team believes a new packing line cuts cycle time. Before: n=30, mean 42 minutes. After: n=30, mean 39 minutes. A two-sample t-test gives p=0.03 at alpha=0.05, so H0 is rejected: the difference is statistically significant. But the 95% CI for the reduction is 0.2 to 5.8 minutes, while the target is 10 minutes. The result is real but not large enough to close the project. The team must also check whether the pilot ran during a low-volume week, which would confound the comparison.
Traps that cost marks
- Treating p<0.05 as proof of practical importance.
- Running many tests and reporting only the significant one.
- Ignoring independence or normality assumptions.
- Using ANOVA on proportions or chi-square on a continuous CTQ.
- Accepting H0 as proof that no effect exists.
- Confusing correlation with causation.
- Updating FMEA risk scores without verifying occurrence or detection.